A Dirac–Dunkl Equation on S[superscript 2] and the Bannai–Ito Algebra
The Dirac–Dunkl operator on the two-sphere associated to the Z[superscript 3][subscript 2] reflection group is considered. Its symmetries are found and are shown to generate the Bannai–Ito algebra. Representations of the Bannai–Ito algebra are constructed using ladder operators. Eigenfunctions of...
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| Language: | English |
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Springer Berlin Heidelberg
2017
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| Online Access: | http://hdl.handle.net/1721.1/106578 |
| _version_ | 1826205131163566080 |
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| author | De Bie, Hendrik Vinet, Luc Genest, Vincent |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics De Bie, Hendrik Vinet, Luc Genest, Vincent |
| author_sort | De Bie, Hendrik |
| collection | MIT |
| description | The Dirac–Dunkl operator on the two-sphere associated to the Z[superscript 3][subscript 2] reflection group is considered. Its symmetries are found and are shown to generate the Bannai–Ito algebra. Representations of the Bannai–Ito algebra are constructed using ladder operators. Eigenfunctions of the spherical Dirac–Dunkl operator are obtained using a Cauchy–Kovalevskaia extension theorem. These eigenfunctions, which correspond to Dunkl monogenics, are seen to support finite-dimensional irreducible representations of the Bannai–Ito algebra. |
| first_indexed | 2024-09-23T13:08:13Z |
| format | Article |
| id | mit-1721.1/106578 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:08:13Z |
| publishDate | 2017 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1065782022-09-28T12:11:17Z A Dirac–Dunkl Equation on S[superscript 2] and the Bannai–Ito Algebra A Dirac–Dunkl Equation on S2 and the Bannai–Ito Algebra De Bie, Hendrik Vinet, Luc Genest, Vincent Massachusetts Institute of Technology. Department of Mathematics Genest, Vincent The Dirac–Dunkl operator on the two-sphere associated to the Z[superscript 3][subscript 2] reflection group is considered. Its symmetries are found and are shown to generate the Bannai–Ito algebra. Representations of the Bannai–Ito algebra are constructed using ladder operators. Eigenfunctions of the spherical Dirac–Dunkl operator are obtained using a Cauchy–Kovalevskaia extension theorem. These eigenfunctions, which correspond to Dunkl monogenics, are seen to support finite-dimensional irreducible representations of the Bannai–Ito algebra. Natural Sciences and Engineering Research Council of Canada 2017-01-20T21:46:18Z 2017-03-01T16:14:48Z 2016-05 2015-01 2016-05-23T12:09:26Z Article http://purl.org/eprint/type/JournalArticle 0010-3616 1432-0916 http://hdl.handle.net/1721.1/106578 De Bie, Hendrik, Vincent X. Genest, and Luc Vinet. “A Dirac–Dunkl Equation on S 2 and the Bannai–Ito Algebra.” Communications in Mathematical Physics 344, no. 2 (May 9, 2016): 447–464. en http://dx.doi.org/10.1007/s00220-016-2648-1 Communications in Mathematical Physics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer-Verlag Berlin Heidelberg application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | De Bie, Hendrik Vinet, Luc Genest, Vincent A Dirac–Dunkl Equation on S[superscript 2] and the Bannai–Ito Algebra |
| title | A Dirac–Dunkl Equation on S[superscript 2] and the Bannai–Ito Algebra |
| title_full | A Dirac–Dunkl Equation on S[superscript 2] and the Bannai–Ito Algebra |
| title_fullStr | A Dirac–Dunkl Equation on S[superscript 2] and the Bannai–Ito Algebra |
| title_full_unstemmed | A Dirac–Dunkl Equation on S[superscript 2] and the Bannai–Ito Algebra |
| title_short | A Dirac–Dunkl Equation on S[superscript 2] and the Bannai–Ito Algebra |
| title_sort | dirac dunkl equation on s superscript 2 and the bannai ito algebra |
| url | http://hdl.handle.net/1721.1/106578 |
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